Workers demonstrating outside PSA Peugeot Citroën's headquarters after the European carmaker announced the closure of the Aulnay factory last year. Photograph: AFP/Getty Images

The dismal scenes that unfolded at Honda's factory in Swindon last week, as staff were told that 800 people were to be fired, have been all too familiar for their fellow car workers across Europe. While resurgent US auto firms will be celebrating their return from the brink at this week's Detroit motor show, thousands of jobs are going at sites in France, Germany and Belgium too, as the industry makes the painful realisation that it is producing far too many cars.

While the names of Aulnay in France, Genk in Belgium and Bochum in Germany are unfamiliar to most drivers in the UK, these are the plants that have produced Citroëns, Fords and Opels for decades. By 2016 they will be closed, victims of the stark fact that western European factories made 16m cars and vans in 2007 but are now churning out vehicles into a market that only sold 12.5m last year.

In France, this realignment with shrunken demand is particularly galling for a country that prides itself on homegrown industrial names such as the now-merged Peugeot and Citroën.

French car sales fell by 14% to 1.9m in 2012, their lowest level for 15 years. The European Automobile Manufacturers' Association is expected to announce that sales declined by 8%-10% in 2012. A double-digit decline would represent the continent's worst performance in nearly two decades.

It is against this backdrop that Honda's Swindon plant, which exports its vehicles to the rest of Europe, is cutting nearly a quarter of its workers. Honda said: "Sustained conditions of low demand in European markets make it necessary to realign Honda's business structure."

At the Peugeot-Citroën factory in the depressed Paris suburb of Aulnay, a community is adjusting to the consequences of the capacity glut. The plant's 3,000-strong workforce is uncertain, fearful and angry. Half of those employed at the site are likely to be laid off when it closes in 2014. The other half have been told they may be retrained or given jobs elsewhere in the company.

However, nobody knows which half they are likely to be in, and with talks between unions and management deadlocked, a debilitating sense of insecurity prevails. Didier Georget, 46, who has worked at Aulnay for 17 years, said: "If this plant closes, it will have a catastrophic effect on the local area, which is already very depressed. We cannot say we feel betrayed because that assumes a relationship with the company owners which has never existed, but we feel as if we are being thrown on the scrapheap."

Vauxhall-Opel, owned by General Motors, has undergone the same process, sparing the Ellesmere Port site on the Wirral but shutting Bochum.

Despite market conditions, there is a deep sense of injustice among the workforce at Aulnay – which specialises in small cars and has turned out more than 8m vehicles since it opened in 1973 – who just a few years ago were being praised for record-breaking production.

Meanwhile, at the home of the US industry in Detroit, executives are preparing to crown their recovery from the depths of the 2008 crisis at the city's annual gathering. US car and light truck sales exceeded 17m at their pre-crisis peak but collapsed to just over 10m in 2009, as the US government was forced to bail out two of the big three US carmakers, General Motors and Chrysler.

That intervention was underpinned by pump-priming of the US economy under the Obama administration that helped to underpin demand for vehicles. Sales rose by 10% in 2010 and 2011 and grew by 13.4% in 2012, to 14.5m.

Apart from a flurry of car scrappage schemes during the credit crunch, the comparison with Europe now is stark.

David Bailey, a car industry expert at Coventry University business school, said: "On the demand side, Obama has put more emphasis on growth rather than austerity and people are more willing to go out and spend money. On the supply side I would argue that American car companies are in a better state because the government intervened."

The European carmakers at Detroit cannot rely on the same state backing. Paul Everitt, chief executive of the UK Society of Motor Manufacturers and Traders, said: "The key European markets are mired in a combination of uncertainty because of the general concerns about the eurozone and the wave of austerity that the individual governments are pursuing. We risk doing irreparable damage to our industrial capability."

The redundancies in Genk, Aulnay, Bochum and now Swindon could be followed by thousands more.